WordNet (r) 3.0 (2006):

bet on
    v 1: place a bet on; "Which horse are you backing?"; "I'm
         betting on the new horse" [syn: bet on, back, gage,
         stake, game, punt]

Moby Thesaurus II by Grady Ward, 1.0:

49 Moby Thesaurus words for "bet on":
   aller sans dire, ante, ante up, back, bank on, be axiomatic,
   be certain, be confident, bet, calculate on, call, count on, cover,
   depend on, doubt not, fade, feel sure, gamble, gamble on,
   go without saying, have no doubt, hazard, just know, know,
   know for certain, lay, lay a wager, lay down, lean on, make a bet,
   meet a bet, parlay, pass, place reliance on, play against, plunge,
   punt, reckon on, rely on, rely upon, repose on, rest assured,
   rest on, see, stake, stand pat, swear by, trust to, wager